Find the solution u(x,y) of a Laplace equation in a rectangle 0 < x < a, 0 < y < b, the boundary and intial conditions are as follows: u(0,y) = 0, u(a,y) = f(y), for 0 < y < b u(x,0) = h(x), u(x,b) = 0, for 0 £ x £ a h(x) = (x/a)2 and f(y) = 1 – (y/b) Consider combining the solutions of two problems, one with homogeneous boundary conditions for u(a,y) = f(y) and the other with homogeneous boundary conditions for u(x,0) = h. (x)

Find the solution u(x,y) of a Laplace equation in a rectangle 0 < x < a, 0 < y < b, the boundary and intial conditions are as follows: u(0,y) = 0, u(a,y) = f(y), for 0 < y < b u(x,0) = h(x), u(x,b) = 0, for 0 £ x £ a h(x) = (x/a)2 and f(y) = 1 – (y/b) Consider combining the solutions of two problems, one with homogeneous boundary conditions for u(a,y) = f(y) and the other with homogeneous boundary conditions for u(x,0) = h. (x)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Find the solution u(x,y) of a Laplace equation in a rectangle 0 < x < a, 0 < y < b, the boundary and intial conditions are as follows:

u(0,y) = 0, u(a,y) = f(y), for 0 < y < b

u(x,0) = h(x), u(x,b) = 0, for 0 £ x £ a

h(x) = (x/a)² and f(y) = 1 – (y/b)

Consider combining the solutions of two problems, one with homogeneous boundary conditions for u(a,y) = f(y) and the other with homogeneous boundary conditions for u(x,0) = h. (x)

Expert Solution